Bekki George Lecture notes 13

# Bekki George Lecture notes 13

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Unformatted text preview: ) n x!in!that!interval,!! f ( x) = f (0) + f ' (0) x + x + ... + x + Rn ( x) ! 2! n! x 1 Where! Rn ( x) is the remainder and Rn ( x) = ∫ f ( n +1) (t )( x − t ) n dt n! 0 Lagrange Formula for Remainder Suppose!f!has!n+1!continuous!derivatives!on!an!open!interval!that!contains!0.!!!Let!x! be!in!that!interval!and!let! Pn ( x) be!the!nth!Taylor!Polynomial!for!f.!!! Then! Rn ( x) = f (n+1) (c ) n+1 x where c is some number between 0 and x. (n + 1)! Example 6: Give!an!error!estimate!for!an!approximation!of!f(x)!=!sin!x\$given!P9(x)!centered!at!! x!=!0!for!x!between!0!a...
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## This note was uploaded on 02/25/2014 for the course MATH 1432 taught by Professor Morgan during the Spring '08 term at University of Houston.

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